$\dfrac{ -10l + 10m }{ -10 } = \dfrac{ -3l - 9n }{ 10 }$ Solve for $l$.
Answer: Notice that the left- and right- denominators are opposite $\dfrac{ -10l + 10m }{ -{10} } = \dfrac{ -3l - 9n }{ {10} }$ So we can multiply both sides by $-10$ $-{10} \cdot \dfrac{ -10l + 10m }{ -{10} } = -{10} \cdot \dfrac{ -3l - 9n }{ {10} }$ $-10l + 10m = - \cdot \left( -3l - 9n \right) $ Distribute the negative sign on the right side. $-10l + 10m = 3l + 9n$ $-{10}l + {10}m = {3}l + {9}n$ Combine $l$ terms on the left. $-{10l} + 10m = {3l} + 9n$ $-{13l} + 10m = 9n$ Move the $m$ term to the right. $-13l + {10m} = 9n$ $-13l = 9n - {10m}$ Isolate $l$ by dividing both sides by its coefficient. $-{13}l = 9n - 10m$ $l = \dfrac{ 9n - 10m }{ -{13} }$ Swap signs so the denominator isn't negative. $l = \dfrac{ -{9}n + {10}m }{ {13} }$